Entropy of Fourier coefficients of periodic musical objects

Abstract

There are many ways to define and measure organization, or complexity, in music, most using the notion of informational entropy, as the opposite of organization. Some researchers prompted me to study whether it could be done from the magnitudes of Fourier coefficients of musical objects (pc-sets or rhythms) instead of addressing their atomic elements (pitches, rhythmic onsets). Indeed I found that it could be a promising new approach to measuring organization of musical material. This note only purports to expose this novel idea, leaving for future research the task of comparing it with the numerous other definitions. I also sketch the study of one relevant basis for such comparisons which has been little explored, the asymptotics of entropy of arithmetic sequences modulo n.